Algebarska proširenja polja

In this thesis we presented the main results of the algebraic field extensions. We have defined algebraic and transcendental extension fields and studied finite extension fields. Since we defined extension fields, naturally raises the question of the existence of algebraic closed fields. We have proven the existence of algebraic closure of each field and that algebraic closure of countable field is also countable. In addition, we showed that any two algebraic closures fields are isomorphic with respect to the defined mapping. We have divided the field types with respect to their characteristics and defined a finite field and its characteristics. We have proved Galois theorem which is an important theorem on finite fields and stated and proved, when are two finite fields isomorphic.